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x^{2}+2y^{2}
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x^{2}+2y^{2}
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x^{2}-4xy+4y^{2}+2y\left(2x-y\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2y\right)^{2}.
x^{2}-4xy+4y^{2}+4yx-2y^{2}
Use the distributive property to multiply 2y by 2x-y.
x^{2}+4y^{2}-2y^{2}
Combine -4xy and 4yx to get 0.
x^{2}+2y^{2}
Combine 4y^{2} and -2y^{2} to get 2y^{2}.
x^{2}-4xy+4y^{2}+2y\left(2x-y\right)
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2y\right)^{2}.
x^{2}-4xy+4y^{2}+4yx-2y^{2}
Use the distributive property to multiply 2y by 2x-y.
x^{2}+4y^{2}-2y^{2}
Combine -4xy and 4yx to get 0.
x^{2}+2y^{2}
Combine 4y^{2} and -2y^{2} to get 2y^{2}.
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